Approximation theorems for stochastic economies with incomplete markets (Q2639758)

This paper shows that for markets which are only approximately complete results obtained for complete markets hold approximately. In particular, it studies robustness in such markets in regard to assumptions related to perfect information or complete observation. Questions concerning perfect competition and Pareto efficiency are also considered. In two sections the author presents the most important notions on which the model rests. Assuming the existence of a limit economy and allowing continuous revisions of trading strategies on the base of improving observations, one examines the behaviour of economies with incomplete markets. For this purpose the notions of epsilon equilibrium and measure of market incompleteness are used. The proof of the main result relies on the representation of martingales by stochastic integrals.